Yes. Material is in the xy plane. Thus TE field means that dominant electric field is in the x or y direction and z component of the electric field is almost zero (or very small value).
I guess there are two things to consider in these simulations: how to excite modes and the effect of BCs. To excite the modes you need to properly choose dipoles’ location and polarization. For example if your dipoles are positioned in the node of a mode, you can not excite that specific mode. Basically you want to properly locate dipoles and their polarization to excite all the modes supported by the structure. However, using symmetric or asymmetric BCs you can suppress TM or TE modes so that you study only a specific type of modes (TE or TM modes).
While I was expecting that you need electric dipoles on the xy plane to properly excite the TE modes, based on your findings and this KX post, it looks like simulation is more sensitive on the location of dipoles (and not much on their polarization), thus your plots look identical. Please note that the band structure plots in your post contains only TE modes and TM modes are suppressed as the result of choosing symmetric BC along z.
Please choose asymmetric BC on the z-direction and update me with your plots. I expect that you get a different bandstructure diagram.
Also this recorded webinar might be very informative.